If you have a card with two analog outputs, you'll be fine. There is no quality loss, the DVI-I-to-VGA adapter is just a passive passthrough. There are difference in quality but you're unlikely to notice much at 15kHz. The one that comes with a GPU was normally better made.
That said, getting things onto various screens can be an interesting exercise. MAME itself or GM is easy enough to set to target a particular display, though. You won't ordinarily be able to use both screens at once, because the focus dictates where the control s are going to. Something like Actual Multiple Monitors display software might help if you want to do two things at once.